Competitive Localization of Vortex Lines and Interacting Bosons

We present a theory for the localization of three-dimensional vortex lines or two-dimensional bosons with a short-ranged repulsive interaction which are competing for a single columnar defect or potential well. For two vortices we use a necklace model approach to find a new kind of delocalization transition between two different states with a single bound particle. This exchange-delocalization transition is characterized by the onset of vortex exchange on the defect for sufficiently weak vortex-vortex repulsion or sufficiently weak binding energy corresponding to high temperature. We calculate the transition point and order of the exchange-delocalization transition. A generalization of this transition to an arbitrary vortex number is proposed.

Figure 1

Two particles binding alternately to a single columnar defect. The particle binding to the defect can be exchanged in localized events, and there are rare collisions between the free and the bound particle.

Figure 2

Schematic phase diagram in the $B\mathrm{\text{−}}T$ plane. $B_m$ is the pristine melting line, $B_{\mathrm{B}\mathrm{G}}$ the Bose glass melting line, and $B_{\mathrm{d}\mathrm{e}}$ the exchange-delocalization crossover line which terminates at $B=0$ in a genuine phase transition at temperature $T_{\mathrm{d}\mathrm{e}}$ (circle).